This invention relates generally to integrated GPS-inertial navigation systems and more specifically to GPS-inertial navigation systems augmented with direction-finding apparatus.
The velocity .nu. of interest in navigating a vehicle relative to the earth using an inertial navigation system is defined by the equation: EQU (d.nu./dt).sub.N =a.sub.sf +g-W.times.(W.times.R)-(W+w).times..nu. (1)
The vector (d.nu./dt).sub.N is the rate of change of the vehicle's velocity relative to the earth expressed in an inertial navigation system frame of reference. An example of a model-based inertial navigation system frame of reference is a local-level system with origin fixed at the point of tangency to the ellipsoidal model of the earth's gravity potential surface at the present position of the vehicle. The ellipsoidal model of the earth's gravity potential surface is called the normal gravity potential (See Heiskenan & Moritz, "Physical Geodesy", Page 67, W. H. Freeman & Co., 1967). The vector a.sub.sf is the specific-force acceleration experienced by the inertial navigation system (INS) on board the vehicle. The vector g is the gravity vector. The vector W is the rotation rate of an earth-fixed frame of reference relative to an inertial frame (i.e. earth's rotation rate vector). The vector R is the position vector of the vehicle from the center of the earth. The vector w is the rotation rate of the inertial navigation system frame relative to the inertial frame.
If the vehicle is stationary with respect to the earth, the equation above becomes: EQU a.sub.sfg +g-W.times.(W.times.R)=0 (2)
Here a.sub.sfg is the specific-force acceleration that balances gravity and the acceleration resulting from the earth's rotation and causes the vehicle to be stationary with respect to the earth. The specific-force acceleration--a.sub.sfg in the stationary case is sometimes referred to as the plumb bob gravity since its direction coincides with that of a plumb bob suspended at the vehicle's present position: EQU a.sub.sfg =-g+W.times.(W.times.R) (3)
The vector a.sub.sfg is only approximately aligned with the local geodetic vertical U which is orthogonal to the normal gravity potential surface of the earth (i.e. the ellipsoidal surface model). The vector a.sub.sfg deviates from the vector U by what is called the deflection of the gravity vertical. The vector U is the vertical axis of what is called the local geodetic frame that is comprised of the orthogonal east, north and vertical axes. The deflection of the vertical is the difference in the slope of the ellipsoidal model of the earth's gravity potential surface with respect to the slope of the actual gravity potential surface, which is called the geoid. The plumb bob gravity is orthogonal to the surface of the geoid.
The vector a.sub.sfg is used to establish the orientation of the level axes of a gravity-based inertial navigation system frame relative to the inertial instrument reference axes during initial alignment of the inertial system. The three orthogonal axes of the inertial system instrument frame usually correspond to the sensing axes of the accelerometers and gyros of the inertial system. The local north component of the earth rate vector W is used to determine the orientation of the inertial navigation frame with respect to the instrument frame in the local level plane relative to the local north axis (i.e. the azimuth orientation). This is achieved by observing the direction of the earth's rotation rate vector about the local north axis during the gyrocompassing phase of initial alignment of the inertial system using a combination of gyro and accelerometer measurements. After initial alignment the orientation of the gravity-based inertial navigation frame relative to the model-based frame differs by small amount due to various sources of error.
After initial alignment, when an inertial navigation system is integrated with a GPS navigation system, the differences in the measurements of position and velocity between the INS and the GPS system can be used to periodically correct the "drift" errors in the inertial system computed position, velocity and orientation with respect to the earth. In addition various causes of such errors, such as due to inertial instrument errors in can also be corrected. In such a situation, a GPS-INS navigation system has been demonstrated to have extremely small errors in position and velocity in actual flight tests. In addition, the error in knowledge of the orientation of the inertial instrument frame, and consequently the gravity-based inertial navigation frame, with respect to the earth is quite small. However, an error does exist in the orientation of the gravity-based inertial system navigation frame about the local north and east geodetic axes. This error which is called the tilt, is caused primarily by the deflection of the gravity vertical. If the highest accuracy navigation performance for a GPS-INS or INS-only (free-inertial) system is to be realized, some means must be developed for conveniently and effectively determining the deflection of the vertical throughout any region of interest. Such data can then be employed for constructing a deflection of the vertical database that can be used to compensate the inertial navigation system accelerometer measurements of force such that the deflection of the vertical has a much reduced effect on the accuracy of the navigation solution.